The Study Of Some Problems In Skew Product Markov

In this paper we discuss the classification of states and the invariant measure in coupling space in skew produce Markov chains.On the aspect of the classification of states,first we study some properties of weak recurrence and the contact between recurrent and properly essential in skew product Markov chains.Secondly we study some results of min-lead which is similar with uniform lead's.Thirdly the decomposition in state space of Markov chains in random environments is studied.Lastly the condition of existence of conservative set and the form of invariant probability are given by the theory of Hopf Chains .On the aspect of the invariant measure in coupling space, we further study the invariant measure in coupling space of skew product Markov chains on the foundation of Li Wei.